Problem: Simplify the following expression: $ z = \dfrac{5}{3} - \dfrac{-2}{a + 1} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{a + 1}{a + 1}$ $ \dfrac{5}{3} \times \dfrac{a + 1}{a + 1} = \dfrac{5a + 5}{3a + 3} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{-2}{a + 1} \times \dfrac{3}{3} = \dfrac{-6}{3a + 3} $ Therefore $ z = \dfrac{5a + 5}{3a + 3} - \dfrac{-6}{3a + 3} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{5a + 5 + 6 }{3a + 3} $ Distribute the negative sign: $z = \dfrac{5a + 5 + 6}{3a + 3}$ $z = \dfrac{5a + 11}{3a + 3}$